Question: Solve for $x$ and $y$ using elimination. ${6x-y = 34}$ ${-5x+y = -28}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the top and bottom equations together. ${x = 6}$ Now that you know ${x = 6}$ , plug it back into $\thinspace {6x-y = 34}\thinspace$ to find $y$ ${6}{(6)}{ - y = 34}$ $36-y = 34$ $36{-36} - y = 34{-36}$ $-y = -2$ $\dfrac{-y}{{-1}} = \dfrac{-2}{{-1}}$ ${y = 2}$ You can also plug ${x = 6}$ into $\thinspace {-5x+y = -28}\thinspace$ and get the same answer for $y$ : ${-5}{(6)}{ + y = -28}$ ${y = 2}$